Gene ranking and biomarker discovery under correlation

Biomarker discovery and gene ranking is a standard task in genomic high throughput analysis. Typically, the ordering of markers is based on a stabilized variant of the t-score, such as the moderated t or the SAM statistic. However, these procedures ignore gene-gene correlations, which may have a profound impact on the gene orderings and on the power of the subsequent tests. We propose a simple procedure that adjusts gene-wise t-statistics to take account of correlations among genes. The resulting correlation-adjusted t-scores ("cat" scores) are derived from a predictive perspective, i.e. as a score for variable selection to discriminate group membership in two-class linear discriminant analysis. In the absence of correlation the cat score reduces to the standard t-score. Moreover, using the cat score it is straightforward to evaluate groups of features (i.e. gene sets). For computation of the cat score from small sample data we propose a shrinkage procedure. In a comparative study comprising six different synthetic and empirical correlation structures we show that the cat score improves estimation of gene orderings and leads to higher power for fixed true discovery rate, and vice versa. Finally, we also illustrate the cat score by analyzing metabolomic data. The shrinkage cat score is implemented in the R package "st" available from URL http://cran.r-project.org/web/packages/st/Comment: 18 pages, 5 figures, 1 tabl

A Score Test for Individual Heteroscedasticity in a One-way Error Components Model

The purpose of this paper is to derive a Rao's efficient score statistic for testing for heteroscedasticity in an error components model with only individual effects. We assume that the individual effect exists and therefore do not test for it. In addition, we assume that the individual effects, and not the white noise term may be heteroscedastic. Finally, we assume that the error components are normally distributed. We first establish, under a specific set of assumptions, the asymptotic distribution of the Score under contiguous alternatives. We then derive the expression for the Score test statistic for individual heteroscedasticity. Finally, we discuss the asymptotic local power of this Score test statistic.panel data; error components model; score test; individual heteroscedasticity: contiguous alternatives; asymptotic local power

Local power of the LR, Wald, score and gradient tests in dispersion models

We derive asymptotic expansions up to order $n^{-1/2}$ for the nonnull distribution functions of the likelihood ratio, Wald, score and gradient test statistics in the class of dispersion models, under a sequence of Pitman alternatives. The asymptotic distributions of these statistics are obtained for testing a subset of regression parameters and for testing the precision parameter. Based on these nonnull asymptotic expansions it is shown that there is no uniform superiority of one test with respect to the others for testing a subset of regression parameters. Furthermore, in order to compare the finite-sample performance of these tests in this class of models, Monte Carlo simulations are presented. An empirical application to a real data set is considered for illustrative purposes.Comment: Submitted for publicatio

Testing for zero-modification in count regression models

Count data often exhibit overdispersion and/or require an adjustment for zero outcomes with respect to a Poisson model. Zero-modified Poisson (ZMP) and zero-modified generalized Poisson (ZMGP) regression models are useful classes of models for such data. In the literature so far only score tests are used for testing the necessity of this adjustment. For this testing problem we show how poor the performance of the corresponding score test can be in comparison to the performance of Wald and likelihood ratio (LR) tests through a simulation study. In particular, the score test in the ZMP case results in a power loss of 47% compared to the Wald test in the worst case, while in the ZMGP case the worst loss is 87%. Therefore, regardless of the computational advantage of score tests, the loss in power compared to the Wald and LR tests should not be neglected and these much more powerful alternatives should be used instead. We also prove consistency and asymptotic normality of the maximum likelihood estimators in the above mentioned regression models to give a theoretical justification for Wald and likelihood ratio tests

Addition of 24‐hour heart rate variability parameters to the Cardiovascular Health Study stroke risk score and prediction of incident stroke: The Cardiovascular Health Study

Background Heart rate variability (HRV) characterizes cardiac autonomic functioning. The association of HRV with stroke is uncertain. We examined whether 24‐hour HRV added predictive value to the Cardiovascular Health Study clinical stroke risk score (CHS‐SCORE), previously developed at the baseline examination. Methods and Results N=884 stroke‐free CHS participants (age 75.3±4.6), with 24‐hour Holters adequate for HRV analysis at the 1994–1995 examination, had 68 strokes over ≤8 year follow‐up (median 7.3 [interquartile range 7.1–7.6] years). The value of adding HRV to the CHS‐SCORE was assessed with stepwise Cox regression analysis. The CHS‐SCORE predicted incident stroke (HR=1.06 per unit increment, P=0.005). Two HRV parameters, decreased coefficient of variance of NN intervals (CV%, P=0.031) and decreased power law slope (SLOPE, P=0.033) also entered the model, but these did not significantly improve the c‐statistic (P=0.47). In a secondary analysis, dichotomization of CV% (LOWCV% ≤12.8%) was found to maximally stratify higher‐risk participants after adjustment for CHS‐SCORE. Similarly, dichotomizing SLOPE (LOWSLOPE <−1.4) maximally stratified higher‐risk participants. When these HRV categories were combined (eg, HIGHCV% with HIGHSLOPE), the c‐statistic for the model with the CHS‐SCORE and combined HRV categories was 0.68, significantly higher than 0.61 for the CHS‐SCORE alone (P=0.02). Conclusions In this sample of older adults, 2 HRV parameters, CV% and power law slope, emerged as significantly associated with incident stroke when added to a validated clinical risk score. After each parameter was dichotomized based on its optimal cut point in this sample, their composite significantly improved prediction of incident stroke during ≤8‐year follow‐up. These findings will require validation in separate, larger cohorts. Keywords: autonomic nervous system, clinical stroke risk model, heart rate variability, prediction, predictors, risk prediction, risk stratification, strok

Acute Spinal Cord Injury: Correlations and Causal Relations Between Intraspinal Pressure, Spinal Cord Perfusion Pressure, Lactate-to-Pyruvate Ratio, and Limb Power.

BACKGROUND/OBJECTIVE: We have recently developed monitoring from the injury site in patients with acute, severe traumatic spinal cord injuries to facilitate their management in the intensive care unit. This is analogous to monitoring from the brain in patients with traumatic brain injuries. This study aims to determine whether, after traumatic spinal cord injury, fluctuations in the monitored physiological, and metabolic parameters at the injury site are causally linked to changes in limb power. METHODS: This is an observational study of a cohort of adult patients with motor-incomplete spinal cord injuries, i.e., grade C American spinal injuries association Impairment Scale. A pressure probe and a microdialysis catheter were placed intradurally at the injury site. For up to a week after surgery, we monitored limb power, intraspinal pressure, spinal cord perfusion pressure, and tissue lactate-to-pyruvate ratio. We established correlations between these variables and performed Granger causality analysis. RESULTS: Nineteen patients, aged 22-70 years, were recruited. Motor score versus intraspinal pressure had exponential decay relation (intraspinal pressure rise to 20 mmHg was associated with drop of 11 motor points, but little drop in motor points as intraspinal pressure rose further, R2 = 0.98). Motor score versus spinal cord perfusion pressure (up to 110 mmHg) had linear relation (1.4 motor point rise/10 mmHg rise in spinal cord perfusion pressure, R2 = 0.96). Motor score versus lactate-to-pyruvate ratio (greater than 20) also had linear relation (0.8 motor score drop/10-point rise in lactate-to-pyruvate ratio, R2 = 0.92). Increased intraspinal pressure Granger-caused increase in lactate-to-pyruvate ratio, decrease in spinal cord perfusion, and decrease in motor score. Increased spinal cord perfusion Granger-caused decrease in lactate-to-pyruvate ratio and increase in motor score. Increased lactate-to-pyruvate ratio Granger-caused increase in intraspinal pressure, decrease in spinal cord perfusion, and decrease in motor score. Causality analysis also revealed multiple vicious cycles that amplify insults to the cord thus exacerbating cord damage. CONCLUSION: Monitoring intraspinal pressure, spinal cord perfusion pressure, lactate-to-pyruvate ratio, and intervening to normalize these parameters are likely to improve limb power

A Combined Score of Circulating miRNAs Allows Outcome Prediction in Critically Ill Patients

Background and aims: Identification of patients with increased risk of mortality represents an important prerequisite for an adapted adequate and individualized treatment of critically ill patients. Circulating micro-RNA (miRNA) levels have been suggested as potential biomarkers at the intensive care unit (ICU), but none of the investigated miRNAs displayed a sufficient sensitivity or specificity to be routinely employed as a single marker in clinical practice. Methods and results: We recently described alterations in serum levels of 7 miRNAs (miR-122, miR-133a, miR-143, miR-150, miR-155, miR-192, and miR-223) in critically ill patients at a medical ICU. In this study, we re-analyzed these previously published data and performed a combined analysis of these markers to unravel their potential as a prognostic scoring system in the context of critical illness. Based on the Youden’s index method, cut-off values were systematically defined for dysregulated miRNAs, and a “miRNA survival score” was calculated. Patients with high scores displayed a dramatically impaired prognosis compared to patients with low values. Additionally, the predictive power of our score could be further increased when the patient’s age was additionally incorporated into this score. Conclusions: We describe the first miRNA-based biomarker score for prediction of medical patients’ outcome during and after ICU treatment. Adding the patients’ age into this score was associated with a further increase in its predictive power. Further studies are needed to validate the clinical utility of this score in risk-stratifying critically ill patients

Misspecified Markov Switching Model

I characterize the local power of an optimal test for a Markov Switching model under generalized alternatives. The result shows that the test still has power for the model with endogenous stochastic parameters unless they are orthogonal to the score functions.